We propose a Level Set Traversal algorithm that iteratively explores regions of high confidence with respect to the input space using orthogonal components of the local gradients.

Full (exact) conformal set vs. split or cross-validated conformal set Non-connectedness of the conformal prediction set. This was initially suggested in [18, Remark 1]. We follow the actual practice in the literature [14, Remark 5]. We did not observe violations. We will also summarize the proposed algorithm in a direct pseudo-code.

Thus, we verify that the random effects estimator is equivalent to the generative model (1). Specifically, if u(x) = 1 for all x X, we use ( X, P,ψ) for simplicity. Due to the separability of ψ, we have the following coreset definition. Definitions 2.2 and 2.3, the regression objectives of OLSE and GLSE can be decomposed into Thus, we can apply the above definition to define coresets for OLSE and GLSE. Now we are ready to describe the FL framework in the language of a query space. We first prove Theorem C.1 and propose the corresponding algorithm that constructs an Next, we prove Theorem C.2 and propose the corresponding algorithm that constructs an accurate Caratheodory's Theorem, there must exist at most To accelerate the running time, Jubran et al. [ By the Caratheodory's Theorem, there must exist at most In this section, we complete the proofs for GLSE.

We thank all reviewers for their encouraging and helpful comments. We will fix all typos. Results are presented in Table A. Following convex relaxation theory[32], our bound has This makes the concretization problem (in Sec. We plan to study high-order bounds on general graphs as our future work. We will also discuss these extensions.

This paper introduces a class of mixed-integer formulations for trained ReLU neural networks.

We present a novel multi-stage workflow for computational materials discovery that achieves a 99% success rate in identifying compounds within 100 meV/atom of thermodynamic stability, with a threefold improvement over previous approaches. By combining the Matra-Genoa generative model, Orb-v2 universal machine learning interatomic potential, and ALIGNN graph neural network for energy prediction, we generated 119 million candidate structures and added 1.3 million DFT-validated compounds to the ALEXANDRIA database, including 74 thousand new stable materials. The expanded ALEXANDRIA database now contains 5.8 million structures with 175 thousand compounds on the convex hull. Predicted structural disorder rates (37-43%) match experimental databases, unlike other recent AI-generated datasets. Analysis reveals fundamental patterns in space group distributions, coordination environments, and phase stability networks, including sub-linear scaling of convex hull connectivity. We release the complete dataset, including sAlex25 with 14 million out-of-equilibrium structures containing forces and stresses for training universal force fields. We demonstrate that fine-tuning a GRACE model on this data improves benchmark accuracy. All data, models, and workflows are freely available under Creative Commons licenses.

The electrocardiogram (ECG) is a vital tool for diagnosing heart diseases. However, many disease patterns are derived from outdated datasets and traditional stepwise algorithms with limited accuracy. This study presents a method for direct cardiovascular disease (CVD) diagnosis from ECG images, eliminating the need for digitization. The proposed approach utilizes a two-step curriculum learning framework, beginning with the pre-training of a classification model on segmentation masks, followed by fine-tuning on grayscale, inverted ECG images. Robustness is further enhanced through an ensemble of three models with averaged outputs, achieving an AUC of 0.9534 and an F1 score of 0.7801 on the BHF ECG Challenge dataset, outperforming individual models. By effectively handling real-world artifacts and simplifying the diagnostic process, this method offers a reliable solution for automated CVD diagnosis, particularly in resource-limited settings where printed or scanned ECG images are commonly used. Such an automated procedure enables rapid and accurate diagnosis, which is critical for timely intervention in CVD cases that often demand urgent care.

Neural Information Processing Systems http://nips.cc/